Following [1]},
we consider a quark star consisting of u, d and s quarks
with masses \(m_{u}=\)  5 MeV, \(m_{d}=\)  7 MeV, and \(m_{s}=\)  100 MeV.
The derivation of the EOS [2]} used here starts with the assumption
that the gluon field can be
decomposed into low (“soft”) and high
(“hard”) momentum components. The expectation values of the soft fields were
identified with the gluon condensates of dimension two and
four, respectively. The former generates a dynamical mass, \(m_G\)  for the hard
gluons,
and the latter yields an analogue of the “bag constant” term
in the energy density and pressure. Given the large number of quark sources,
even in
the weak coupling regime, the hard gluon fields
are strong, the occupation numbers are large, and therefore these fields can be
approximated by classical color fields.
The effect of the condensates is to soften the EOS whereas the hard gluons
significantly
stiffen it, by increasing both the energy density and pressure. With these
approximations it was possible to derive [2]} an analytical expression
for the EOS, called MFTQCD (Mean Field Theory of QCD). When adapting this
equation of state to the stellar medium, we assume, as usual, that quarks and
electrons are in chemical equilibrium maintained by the weak
processes [4]}.
Neutrinos are assumed to escape and do not contribute to the pressure and
energy density.
Moreover, we impose charge neutrality and baryon number conservation.
These requirements yield a set of four algebraic equations for Fermi
momentum calculation for each quark flavor (\(u\) , \(d\)  and \(s\) ) and for the
electrons (\(e\) )
\({k_{u}}^{3}+{k_{d}}^{3}+{k_{s}}^{3}=3\pi ^{2}\rho _{B},\) 
\(2{k_{u}}^{3}={k_{d}}^{3}+{k_{s}}^{3}+{k_{e}}^{3},\) 
\({k_{d}}^{2}+{m_{d}}^{2}={k_{s}}^{2}+{m_{s}}^{2},\) 
\(\sqrt{{k_{u}}^{2}+{m_{u}}^{2}}+\sqrt{{k_{e}}^{2}+{m_{e}}^{2}}=\sqrt{{k_{s}}^{2}+{m_{s}}^{2}},\) 
